a straight line d from Q to A.
Translate line d --> d’, so point P is at origin
Let R be the intersection point on AB of line d’.
Draw a straight line through Q to R.
Area RBQ = Area ARQC
P midpoint of BC
AQ // PR
Triangles ARP and RPQ share the same height h and base
Area of Δ ARP = Area of Δ RPQ
Δ ABP = Δ RBP + Δ ARP
= Δ RBP + Δ RPQ
Area RBQ = Area ABP = Area ABC/2
Consequently: Area RBQ = Area ARQC
Please spread the word about the Sunday Puzzle!